Problem: Simplify the following expression: $q = \dfrac{5r}{4} + \dfrac{9r}{5}$
Solution: In order to add expressions, they must have a common denominator. The smallest common denominator is the least common multiple of $4$ and $5$ $\lcm(4, 5) = 20$ $ q = \dfrac{5}{5} \cdot \dfrac{5r}{4} + \dfrac{4}{4} \cdot \dfrac{9r}{5} $ $q = \dfrac{25r}{20} + \dfrac{36r}{20}$ $q = \dfrac{25r +36r}{20}$ $q = \dfrac{61r}{20}$